In this paper we investigate the non-linear binding effects upon the diffusion-migration test. For the diffusion test we derive the conditions required for the non-linear binding isotherm to produce an actual penetration front. When more than two ion species are present we show that the diffusion coefficient associated with a particular ion cannot be extracted from the diffusion test on account of multi-species electrical effects. In the migration test where an external electrical field is applied to the sample, we give the conditions required for the propagation of a stable 'travelling wave'. In addition new explicit expressions of the time-lag are obtained for both tests, allowing the determination of the properties of the unknown binding isotherm whatever its physical nature. Throughout the paper the results and the method are illustrated by the diffusion of the Cl- ion within cement-based materials, using experimental data extracted from literature. The theoretical predictions compare well to these experimental data.